Method for predicting residual life of degraded equipment by considering influence of hybrid measurement error

Abstract

The invention provides a degraded equipment residual life prediction method considering the influence of a hybrid measurement error, and relates to the technical field of equipment residual life prediction, and the method comprises the steps: constructing a nonlinear random degradation model with the hybrid measurement error based on a nonlinear Wiener process of random degraded equipment; calculating parameters of the nonlinear stochastic degradation model by using a particle expectation maximization algorithm and a nonlinear stochastic degradation model parameter adaptive estimation algorithm based on particle filtering to obtain a model parameter vector; and based on a nonlinear random degradation model and the model parameter vector, considering the influence of the hybrid measurement error, performing adaptive prediction on the residual life of the random degradation equipment to obtain a residual life prediction result, and completing prediction of the residual life of the random degradation equipment. The problem that the residual life prediction result of the random degradation equipment is not high in accuracy is solved.

Description

Technical Field

[0001] The present specification relates to the technical field of equipment remaining life prediction, and in particular to a method for predicting the remaining life of degraded equipment taking into account the influence of mixed measurement errors. Background Art

[0002] As an ideal actuator for attitude control systems, the Control Moment Gyro (CMG) has the advantages of large output torque and low power consumption. It is widely used in spacecraft such as satellites, spacecrafts, and space stations. During the life cycle of the gyro, the bearing is subjected to long-term effects of factors such as fatigue and wear, which causes its support performance to gradually degrade. This performance degradation is directly related to the working accuracy and life of the gyro. Therefore, the amount of bearing wear can be used as the performance degradation amount in the prediction of gyro life. However, the amount of bearing wear during the satellite's in-orbit period is usually not directly measured, but the degree of bearing wear can be reflected by observable characteristic quantities such as temperature and motor current. When the characteristic quantity degrades to a certain threshold, the degree of bearing wear can be estimated according to certain models to infer the life of the gyro. According to the mechanism failure analysis, temperature is the result of frictional heat generation, heat generation by viscous resistance of the lubricating oil film, and the working effects of environmental factors. During the operation of the control moment gyro, friction during the operation of the bearing is inevitable. As the high-speed component flywheel rotates at high speed, the friction resistance between the bearing and the cage will generate a large amount of frictional heat, which is manifested externally as a gradual increase in high-speed shaft temperature until it reaches the failure threshold.

[0003] Usually, temperature sensors are used to collect data on the temperature changes of satellite moment gyros. Due to non-ideal measurement factors, the monitored degradation data is inevitably affected by the measurement process. In addition, when satellite monitoring data is transmitted to the ground, it is usually necessary to perform analog-to-digital conversion or direct digital measurement. Affected by factors such as the number of analog-to-digital conversion bits and the conversion range, the actual acquired telemetry data may have quantization errors. When the acquired temperature rise data exceeds the failure threshold, it is considered that the performance of the control moment gyro of this type of satellite has degraded and failed. In the actual data monitoring process, due to the existence of measurement errors and quantization errors, the acquired state monitoring data has certain deviations, which directly affects the accuracy of the remaining life prediction. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for predicting the remaining life of degraded equipment taking into account the influence of mixed measurement errors, which solves the problem of low accuracy of the remaining life prediction results of randomly degraded equipment.

[0005] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors, comprising:

[0006] S1: Based on the nonlinear Wiener process of randomly degraded equipment, a nonlinear random degradation model with mixed measurement errors is constructed;

[0007] S2: using a particle expectation maximization algorithm and a nonlinear random degradation model parameter adaptive estimation algorithm based on particle filtering to calculate the parameters of the nonlinear random degradation model to obtain a model parameter vector;

[0008] S3: Based on the nonlinear random degradation model and the model parameter vector, considering the influence of mixed measurement errors, the remaining life of the randomly degraded equipment is adaptively predicted to obtain a remaining life prediction result, thereby completing the prediction of the remaining life of the randomly degraded equipment.

[0009] The beneficial effects of the present invention are as follows: the processor uses the nonlinear Wiener process of the randomly degraded device to construct a nonlinear random degradation model with mixed measurement errors, and predicts the remaining life of the randomly degraded device by calculating the model parameter vector to obtain the remaining life prediction result. In this way, each degradation data can be used to adaptively estimate the model parameters to achieve online update of the remaining life prediction; by overcoming the influence of data mixing errors, a more accurate remaining life prediction result of the randomly degraded device can be obtained.

[0010] Furthermore, the S1 includes:

[0011] The nonlinear Wiener process is used to analyze the random degradation equipment and obtain the real degradation process of the equipment;

[0012] By taking into account normal random errors and quantization errors, the real degradation process of the device is adjusted to obtain the actual measurement process of the device;

[0013] Based on the interaction between the internal factors of individual differences of equipment and the external environment, the nonlinear random degradation model with mixed measurement errors is constructed using the drift coefficient.

[0014] Furthermore, the expression of the nonlinear random degradation model is:

[0015]

[0016] Among them, λ k represents the drift coefficient of the kth monitoring point, λ k-1 represents the drift coefficient of the k-1th monitoring point, x k represents the potential degradation state of the equipment at the kth monitoring point, x k-1 represents the potential degradation state of the equipment at the k-1th monitoring point, t k represents the monitoring time corresponding to the kth monitoring point, μ represents the nonlinear function form, τ represents time, θ represents the random parameter, and t k-1represents the monitoring time corresponding to the k-1th monitoring point, σ B represents the diffusion coefficient of the degradation process, B represents the Brownian motion, Represents device measurement data, ε k represents the measurement error, y k represents the actual observed data of the equipment during the quantization process, e k Represents the quantization error.

[0017] Further, the S2 includes:

[0018] S210: Use the particle smoothing algorithm to adjust the particle importance weight to obtain the particle smoothing density:

[0019]

[0020] Among them, p(z m ∣Θ,Y 1:k ) represents the particle smoothing density, z m represents the hidden state, Θ represents the unknown parameter vector of the model, Y 1:k represents the actual observation data from the 1st point to the kth point, represents the normalized weight, δ represents the Dirac function, represents the sampled particle, i represents the i-th sampling, m represents 1, 2, ... k, k represents the k-th monitoring point, and N represents the total number of sampling times;

[0021] S220: using a particle expectation maximization algorithm, iterating an estimation process of a model parameter vector of the nonlinear random degradation model to obtain a maximum estimation result of the model parameter vector;

[0022] S230: Calculate and obtain parameter estimation results using a nonlinear random degradation model parameter adaptive estimation algorithm based on particle filtering and the particle smoothing density;

[0023] S240: Using the parameter estimation result, the maximum estimation result of the model parameter vector is updated, and the model parameter vector is obtained by a gradient descent search method.

[0024] Furthermore, the expression of the maximum estimation result of the model parameter vector is:

[0025]

[0026] in, Indicates that based on the observed data Y 1:k The qth iteration result of represents the maximization parameter, It means to calculate about p(z k ,Y 1:k|Θ), p(z k ,Y 1:k |Θ) represents the joint likelihood function, z k represents the implicit state of the k-th monitoring point model, Y 1:k represents the actual observation data from the 1st point to the kth point, Θ represents the unknown parameter vector of the model, and q represents the number of iterations.

[0027] Furthermore, the expression of the parameter estimation result is:

[0028]

[0029] in, represents the expectation of the joint likelihood function, Θ represents the unknown parameters of the model, Indicates that based on the observed data Y 1:k The qth iteration result of represents the conditional expectation of the joint likelihood function, p(z k ,Y 1:k |Θ) represents the joint likelihood function, z k represents the implicit state of the k-th monitoring point model, Y 1:k represents the actual observation data from the 1st point to the kth point, Θ represents the unknown parameters of the model, p(z1|z0,Θ) represents the prior distribution of the implicit state of the first monitoring point, z1 represents the implicit state of the first monitoring point, z0 represents the initial implicit state, p(z m+1 |z m ,Θ) represents the prior distribution of the implicit state of the m+1th monitoring point, z m+1 represents the implicit state of the mth monitoring point, z m represents the implicit state of the mth monitoring point, p(y m |z m ,Θ) represents the observation data y m The joint PDF of y m represents the observation data of the mth monitoring point, m represents the mth monitoring point, k represents the kth monitoring point, and q represents the number of iterations.

[0030] Furthermore, the gradient calculation expression of the model parameter vector is:

[0031]

[0032] in, represents the expectation of the joint likelihood function, Θ represents the unknown parameters of the model, Indicates that based on the observed data Y 1:k The qth iteration result, q represents the number of iterations, and Represent the three parts of the joint log-likelihood function respectively.

[0033] Further, the S3 includes:

[0034] According to the random degradation process, the remaining life function of the equipment is constructed;

[0035] Based on the nonlinear random degradation model, the implicit state of the model is obtained by sampling the prior distribution, and the probability density function corresponding to the prior distribution function and the actual measurement data is obtained;

[0036] Based on the prior distribution function and the probability density function corresponding to the actual measurement data, the posterior distribution function is approximated using standard importance weights;

[0037] The model parameter vector, the equipment remaining life function and the posterior distribution function are used to adaptively predict the remaining life of the randomly degraded equipment by considering the influence of mixed measurement errors to obtain a remaining life prediction result.

[0038] Furthermore, the expression of the equipment remaining life function is:

[0039] L k = inf{l k :Y(l k +t k )≥w|Y(t k ) <w};

[0040] The expression of the probability density function corresponding to the actual measurement data is:

[0041]

[0042] The expression of the standard importance weight is:

[0043]

[0044] Among them, L k represents the remaining life of the kth monitoring point, inf represents the infimum, l k represents the remaining life of the kth monitoring point, Y(l k +t k ) means l k +t k The degenerate state corresponding to the moment, t k represents the duration corresponding to the kth monitoring point, w represents the failure threshold, Y(t k ) indicates t k The degenerate state corresponding to the moment, Represents the observed data y k The joint PDF of y k represents the observation data of the kth monitoring point, represents the implicit state, Θ represents the unknown parameter vector of the model, a represents the lower bound of the quantization error, b represents the upper bound of the quantization error, Indicates e k PDF, e k represents the quantization error, Represents ε k PDF, ε k represents the measurement error, σ ε represents the standard deviation of measurement error, exp represents the exponential form of a natural constant, represents the potential degradation state, q represents the quantization range, Φ represents the cumulative distribution function of the standard normal distribution, represents the k-th criterion importance weight, represents the k-1th standard importance weight, and Φ represents the cumulative distribution function of the standard normal distribution.

[0045] Furthermore, the expression of the remaining life prediction result is:

[0046]

[0047] in, The PDF of the remaining life, L k Remaining life, l k represents the remaining life, Θ represents the unknown parameter vector of the model, Y 1:k represents the observation data of the 1st to kth monitoring points, represents the normalized weight, ω represents the failure threshold, represents the potential degradation state of the kth point, represents the k-th point drift coefficient, t k represents the kth point monitoring time, l k represents the remaining life, μ represents the nonlinear function form, τ represents time, θ represents the random parameter, exp represents the exponential function with e as the base, σ B represents the diffusion coefficient, i represents the i-th sampling, k represents the number of monitoring points, and N represents the number of sampling times. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] This specification will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:

[0049] Figure 1 It is an exemplary flow chart of a method for predicting the remaining life of a degraded device taking into account the influence of mixed measurement errors according to some embodiments of this specification. DETAILED DESCRIPTION

[0050] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0051] Example

[0052] Figure 1 is an exemplary flow chart of a method for predicting the remaining life of a degraded device considering the influence of mixed measurement errors according to some embodiments of this specification. Figure 1 As shown, the process includes the following steps. In some embodiments, the process can be executed by a processor.

[0053] S1: Based on the nonlinear Wiener process of randomly degraded equipment, a nonlinear random degradation model with mixed measurement errors is constructed.

[0054] Randomly degraded devices are devices with limited operating life that are affected by internal factors of the device and the external environment. For example, randomly degraded devices may include aircraft engines, lithium batteries, inertial navigation system gyroscopes, and ball bearings.

[0055] The nonlinear Wiener process is a process used to characterize the true degradation of a device.

[0056] Mixed measurement errors are a combination of errors generated during the equipment monitoring process. For example, mixed measurement errors can include normal random errors and quantization errors.

[0057] The nonlinear random degradation model is a mathematical model that reflects the degradation of random degradation equipment while taking into account measurement uncertainty and nonlinearity.

[0058] In some embodiments, the processor can use a nonlinear Wiener process to analyze a randomly degraded device to obtain a true degradation process of the device; by considering normal random errors and quantization errors, the true degradation process of the device is adjusted to obtain an actual measurement process of the device; based on the interaction between internal factors of individual differences in the device and the external environment, the drift coefficient is used to construct the nonlinear random degradation model with mixed measurement errors.

[0059] The actual degradation process of equipment is non-monotonic, nonlinear and random.

[0060] In some embodiments, the expression of the actual degradation process of the device can be:

[0061]

[0062] Where X(t) represents the degradation state of the device at time t, t represents time t, and X(0) represents the initial degradation state of the device. represents the drift term of the degradation process, λ is the drift coefficient, which is used to represent the individual characteristics of the degradation of the same batch of equipment, μ represents the nonlinear function form, τ represents time, θ represents the random parameter, σ B It represents the diffusion coefficient of the degradation process, represents the common characteristics of the degradation of the same batch of equipment, and B(t) represents the standard Brownian motion.

[0063] Normal random error is the random measurement error of the monitoring data at each moment that follows the normal distribution.

[0064] Quantization error is the error caused by analog-to-digital conversion or digital measurement of monitoring data at each moment.

[0065] The actual measurement process of the device is the device measurement process taking into account the mixed measurement errors.

[0066] In some embodiments, the expression of the actual measurement process of the device can be:

[0067]

[0068] in, represents the monitoring data with sensor measurement error, Y(t) represents the actual monitoring data under the action of quantization error, ε t represents the normal random error of the monitoring data corresponding to time t, e t Represents the quantization error of the monitoring data corresponding to time t.

[0069] In some embodiments, the quantization error e t The corresponding probability density function expression can be:

[0070]

[0071] Among them, f e (e) represents the quantization error e t The corresponding probability density, e represents the natural constant, q represents the quantization range; q=ba, a and b represent the upper and lower limits of the quantization range.

[0072] The internal factors of individual differences of equipment are the equipment’s own parameters and structural factors.

[0073] The external environment refers to the environmental information such as temperature and humidity around the device.

[0074] The drift coefficient is used to eliminate the error caused by the interaction between the internal factors of different devices and the external environment.

[0075] In some embodiments, the processor may use the drift coefficient as a random parameter of a Gaussian distribution to construct a nonlinear random degradation model with mixed measurement errors.

[0076] In some embodiments, the expression of the nonlinear random degradation model may be:

[0077]

[0078] Among them, λ k represents the drift coefficient of the kth monitoring point, λ k-1 represents the drift coefficient of the k-1th monitoring point, x k represents the potential degradation state of the equipment at the kth monitoring point, x k-1 represents the potential degradation state of the equipment at the k-1th monitoring point, t k represents the monitoring time corresponding to the kth monitoring point, μ represents the nonlinear function form, τ represents time, θ represents the random parameter, and t k-1 represents the monitoring time corresponding to the k-1th monitoring point, σ B represents the diffusion coefficient of the degradation process, B represents the Brownian motion, Represents device measurement data, ε k represents the measurement error, y k represents the actual observed data of the equipment during the quantization process, e k Represents the quantization error.

[0079] S2: Calculate the parameters of the nonlinear random degradation model by using a particle expectation maximization algorithm and a nonlinear random degradation model parameter adaptive estimation algorithm based on particle filtering to obtain a model parameter vector.

[0080] The particle expectation-maximization algorithm (particle EM algorithm) is an algorithm for estimating model parameters through E-step and M-step calculations.

[0081] The particle filter-based nonlinear random degradation model parameter adaptive estimation algorithm is an algorithm for obtaining the model parameter vector through parameter derivation.

[0082] The model parameter vector is a vector consisting of the unknown parameters of the model. For example, the model parameter vector may include μ λ , σ λ , the diffusion term of the degradation process σ B , σ ε and parameters such as the common characteristics θ of the degradation of the same batch of equipment.

[0083] In some embodiments, the expression of the model parameter vector may be:

[0084] In some embodiments, the expression of the log-likelihood function of the model parameter vector may be:

[0085] l k (Θ)=ln p(Y 1:k |Θ);

[0086] Among them, l k (Θ) represents the log-likelihood function of the model parameter vector, p(Y 1:k |Θ) represents the observed data Y 1:k The joint probability density function, Y 1:k Represents the actual observation data from the 1st point to the kth point.

[0087] In some embodiments, the processor may implement S2 based on the following steps.

[0088] S210: Using a particle smoothing algorithm to adjust the particle importance weight to obtain a particle smoothing density.

[0089] The particle smoothing algorithm is an algorithm used to calculate the smoothed density of particles.

[0090] Particle importance weight is a parameter that reflects the importance between particles.

[0091] Particle smoothing density is a parameter that reflects the particle density during particle smoothing.

[0092] In some embodiments, the expression for particle smoothing density may be:

[0093]

[0094] Among them, p(z m ∣Θ,Y 1:k ) represents the particle smoothing density, z m represents the hidden state, Θ represents the unknown parameter vector of the model, Y 1:k represents the actual observation data from the 1st point to the kth point, represents the normalized weight, δ represents the Dirac function, represents the sampled particle, i represents the i-th sampling, m represents 1, 2, …k, k represents the k-th monitoring point, and N represents the total number of sampling times.

[0095] In some embodiments, the processor may calculate the particle importance weight using a conditional probability formula:

[0096]

[0097] In some embodiments, the processor may process the particle smoothing density using the total probability formula and the Bayesian formula to obtain a processing result:

[0098]

[0099] When m=k, the smoothed density p(z m |Θ,Y 1:k ) and the posterior distribution p(z k |Θ,Y 1:k ) are equal, at this time the particle smoothing weight And the particles used Same.

[0100] In some embodiments, the integral term in the particle smoothing density can be calculated by backward iteration:

[0101]

[0102] Among them, Y 1:m represents the actual observation data from the 1st point to the mth point, represents the normalized weight at time m+1, represents the normalized weight at time m, Represents the implicit state at time m.

[0103] In some embodiments, The expression can be:

[0104]

[0105] S220: using a particle expectation maximization algorithm, iterating the estimation process of the model parameter vector of the nonlinear random degradation model to obtain a maximum estimation result of the model parameter vector.

[0106] The maximum estimate of the model parameter vector is the estimate that is closest to the actual model parameter vector.

[0107] In some embodiments, the expression for the maximum estimation result of the model parameter vector may be:

[0108]

[0109] in, represents the maximum estimation result of the model parameter vector, represents the maximum value function and l(Θ) represents .

[0110] In some embodiments, the processor may obtain the conditional log-likelihood function of the model parameter vector Θ through E-step calculation:

[0111]

[0112] in, represents the conditional log-likelihood function of the model parameter vector Θ, express.

[0113] In some embodiments, the expression of the logarithmic joint likelihood function in step E may be:

[0114]

[0115] In some embodiments, by calculating the conditional mathematical expectation of the logarithmic joint likelihood function in step E, it can be obtained:

[0116]

[0117] The expression of the unknown parameter is:

[0118]

[0119] In some embodiments, the processor may obtain the maximum estimation result of the model parameter vector through M-step calculation:

[0120]

[0121] in, Indicates that based on the observed data Y 1:k The qth iteration result of represents the maximization parameter, It means to calculate about p(z k ,Y 1:k |Θ), p(z k ,Y 1:k |Θ) represents the joint likelihood function, z k represents the implicit state of the k-th monitoring point model, Y 1:k represents the actual observation data from the 1st point to the kth point, Θ represents the unknown parameter vector of the model, and q represents the number of iterations.

[0122] In some embodiments, the processor may iterate the E step and the M step until the function converges to obtain a maximum estimation result of the final model parameter vector.

[0123] S230: Calculate and obtain parameter estimation results using a particle filter-based nonlinear random degradation model parameter adaptive estimation algorithm and the particle smoothing density.

[0124] The parameter estimation result is the conditional log-likelihood function of the model parameter vector Θ obtained in the E step.

[0125] In some embodiments, the expression of the parameter estimation result may be:

[0126]

[0127] in, represents the expectation of the joint likelihood function, Θ represents the unknown parameters of the model, Indicates that based on the observed data Y 1:k The qth iteration result of represents the conditional expectation of the joint likelihood function, p(z k ,Y 1:k |Θ) represents the joint likelihood function, z k represents the implicit state of the k-th monitoring point model, Y 1:k represents the actual observation data from the 1st point to the kth point, Θ represents the unknown parameters of the model, p(z1|z0,Θ) represents the prior distribution of the implicit state of the first monitoring point, z1 represents the implicit state of the first monitoring point, z0 represents the initial implicit state, p(z m+1 |z m ,Θ) represents the prior distribution of the implicit state of the m+1th monitoring point, z m+1 represents the implicit state of the mth monitoring point, z m represents the implicit state of the mth monitoring point, p(y m |z m ,Θ) represents the observation data y m The joint PDF of y m represents the observation data of the mth monitoring point, m represents the mth monitoring point, k represents the kth monitoring point, and q represents the number of iterations.

[0128] S240: Using the parameter estimation result, the maximum estimation result of the model parameter vector is updated, and the model parameter vector is obtained by a gradient descent search method.

[0129] In some embodiments, the processor may use the processing result of the E step to iteratively update the maximum estimation result of the model parameter vector obtained in the M step to obtain the maximum estimation result of the updated model parameter vector.

[0130] The gradient descent search method is an iterative algorithm for solving for model parameters.

[0131] In some embodiments, the gradient calculation expression of the model parameter vector may be:

[0132]

[0133] in, represents the expectation of the joint likelihood function, Θ represents the unknown parameters of the model, Indicates that based on the observed data Y 1:k The qth iteration result, q represents the number of iterations, and Represent the three parts of the joint log-likelihood function respectively.

[0134] In some embodiments, and The expression can be:

[0135]

[0136] S3: Based on the nonlinear random degradation model and the model parameter vector, considering the influence of mixed measurement errors, the remaining life of the randomly degraded equipment is adaptively predicted to obtain a remaining life prediction result, thereby completing the prediction of the remaining life of the randomly degraded equipment.

[0137] The remaining life prediction result is the prediction result reflecting the remaining life time of randomly degraded equipment.

[0138] In some embodiments, the processor can construct a device remaining life function based on a random degradation process; based on the nonlinear random degradation model, obtain the model implicit state by sampling the prior distribution, and obtain the probability density function corresponding to the prior distribution function and the actual measurement data; based on the prior distribution function and the probability density function corresponding to the actual measurement data, use the standard importance weight to approximate the posterior distribution function; use the model parameter vector, the device remaining life function and the posterior distribution function, consider the influence of mixed measurement errors, and adaptively predict the remaining life of the randomly degraded device to obtain a remaining life prediction result.

[0139] The equipment remaining life function is a function that reflects the relationship between the equipment remaining life and time.

[0140] In some embodiments, the expression of the device remaining life function is:

[0141] L k = inf{l k :Y(l k +t k )≥w|Y(t k ) <w};

[0142] Among them, L k represents the remaining life of the kth monitoring point, inf represents the infimum, l k represents the remaining life of the kth monitoring point, Y(l k +t k ) indicates l k +t k The degenerate state corresponding to the moment, t k represents the duration corresponding to the kth monitoring point, w represents the failure threshold, Y(t k ) indicates t k The degraded state corresponding to the moment.

[0143] The model implicit state is the parameter state implicit in the nonlinear stochastic degradation model. For example, the model implicit state may include the potential degradation state xk and the random parameter λ k wait.

[0144] In some embodiments, the processor may estimate the state of the nonlinear random degradation model using actual measurement data to obtain the model implicit state.

[0145] The prior distribution function is a function that reflects the distribution of particles in the discrete state space.

[0146] In some embodiments, the expression of the prior distribution function may be:

[0147]

[0148] in, represents the drift coefficient of the kth monitoring point, represents the drift coefficient of the k-1th monitoring point, represents the initial drift coefficient, u λ represents the mean value of drift coefficient, σ λ Indicates the standard deviation of the drift coefficient.

[0149] The probability density function corresponding to the actual measured data is a function that reflects the probability density of the actual measured data.

[0150] In some embodiments, the probability density corresponding to the actual measurement data can be expressed as:

[0151]

[0152] Among them, y k represents the observation data of the kth monitoring point, x k represents the potential degradation state of the kth monitoring point, ε k represents the measurement error, e k represents the quantization error, and y k 、x k , ε k and e k The PDF of k , ε k Obeying Gaussian distribution, e k Obey uniform distribution.

[0153] In some embodiments, the processor may obtain a probability density function corresponding to the actual measurement data based on the model implicit state and the model parameter vector:

[0154]

[0155] in, Represents the observed data yk The joint PDF of y k represents the observation data of the kth monitoring point, represents the implicit state, Θ represents the unknown parameter vector of the model, a represents the lower bound of the quantization error, b represents the upper bound of the quantization error, Indicates e k PDF, e k represents the quantization error, Represents ε k PDF, ε k represents the measurement error, σ ε represents the standard deviation of measurement error, exp represents the exponential form of a natural constant, represents the potential degradation state, q represents the quantization range, and Φ represents the cumulative distribution function of the standard normal distribution.

[0156] The standard importance weight is a parameter that reflects the importance of the particle.

[0157] In some embodiments, the expression of the standard importance weight may be:

[0158]

[0159] in, represents the k-th criterion importance weight, represents the k-1th standard importance weight, and Φ represents the cumulative distribution function of the standard normal distribution.

[0160] In some embodiments, the expression of the normalized importance weight may be:

[0161]

[0162] The posterior distribution function is a particle distribution function constructed based on particle samples and the corresponding standard importance weights. For example, the expression of the posterior distribution function can be:

[0163]

[0164] In some embodiments, the processor may use the model parameter vector, the device remaining life function and the posterior distribution function, and consider the influence of mixed measurement errors to adaptively predict the remaining life of the randomly degraded device to obtain a remaining life prediction result:

[0165]

[0166] in, Indicates that given the model parameter vector Θ and the degradation data Y 1:k Under the condition of k The conditional mathematical expectation of .

[0167] In some embodiments, the expression of the remaining life prediction result can be:

[0168]

[0169] in, The PDF of the remaining life, L k Remaining life, l k represents the remaining life, Θ represents the unknown parameter vector of the model, Y 1:k represents the observation data of the 1st to kth monitoring points, represents the normalized weight, ω represents the failure threshold, represents the potential degradation state of the kth point, represents the k-th point drift coefficient, t k represents the kth point monitoring time, l k represents the remaining life, μ represents the nonlinear function form, τ represents time, θ represents the random parameter, exp represents the exponential function with e as the base, σ B represents the diffusion coefficient, i represents the i-th sampling, k represents the number of monitoring points, and N represents the number of sampling times.

[0170] In some embodiments, for the random degradation process {Y(t), t≥0} under the influence of quantization error and normal measurement error, if the drift coefficient follows a normal distribution The remaining equipment life PDFs predicted by the two nonlinear models H1 and H2 are:

[0171]

[0172]

[0173] in, The PDF of the remaining life of model H1, η(l k ) represents the time interval in nonlinear form, The PDF representing the remaining life of model H2.

[0174] Model H1 is a random degradation power model that takes into account the influence of mixed measurement errors.

[0175] Model H2 is a random degradation exponential model that takes into account the influence of mixed measurement errors.

[0176] In some embodiments of the present specification, the processor uses the nonlinear Wiener process of the randomly degraded device to construct a nonlinear random degradation model with mixed measurement errors, and predicts the remaining life of the randomly degraded device by calculating the model parameter vector to obtain the remaining life prediction result. In this way, each degradation data can be used to adaptively estimate the model parameters to achieve online update of the remaining life prediction; by overcoming the influence of data mixing errors, a more accurate remaining life prediction result of the randomly degraded device can be obtained.

Claims

1. A method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors, characterized in that: include: S1: Based on the nonlinear Wiener process of randomly degraded equipment, a nonlinear random degradation model with mixed measurement errors is constructed; S2: using a particle expectation maximization algorithm and a nonlinear random degradation model parameter adaptive estimation algorithm based on particle filtering to calculate the parameters of the nonlinear random degradation model to obtain a model parameter vector; S3: Based on the nonlinear random degradation model and the model parameter vector, considering the influence of mixed measurement errors, the remaining life of the randomly degraded equipment is adaptively predicted to obtain a remaining life prediction result, thereby completing the prediction of the remaining life of the randomly degraded equipment.

2. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 1 is characterized in that: The S1 includes: The nonlinear Wiener process is used to analyze the random degradation equipment and obtain the real degradation process of the equipment; By taking into account normal random errors and quantization errors, the real degradation process of the device is adjusted to obtain the actual measurement process of the device; Based on the interaction between the internal factors of individual differences of equipment and the external environment, the nonlinear random degradation model with mixed measurement errors is constructed using the drift coefficient.

3. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 1 is characterized in that: The expression of the nonlinear random degradation model is: Among them, λ k represents the drift coefficient of the kth monitoring point, λ k-1 represents the drift coefficient of the k-1th monitoring point, x k represents the potential degradation state of the equipment at the kth monitoring point, x k-1 represents the potential degradation state of the equipment at the k-1th monitoring point, t k represents the monitoring time corresponding to the kth monitoring point, μ represents the nonlinear function form, τ represents time, θ represents the random parameter, and t k-1 represents the monitoring time corresponding to the k-1th monitoring point, σ B represents the diffusion coefficient of the degradation process, B represents the Brownian motion, Represents device measurement data, ε k represents the measurement error, y k represents the actual observed data of the equipment during the quantization process, e k Represents the quantization error.

4. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 1 is characterized in that: The S2 includes: S210: Use the particle smoothing algorithm to adjust the particle importance weight to obtain the particle smoothing density: Among them, p(z m ∣Θ,Y 1:k ) represents the particle smoothing density, z m represents the hidden state, Θ represents the unknown parameter vector of the model, Y 1:k represents the actual observation data from the 1st point to the kth point, represents the normalized weight, δ represents the Dirac function, represents the sampled particle, i represents the i-th sampling, m represents 1, 2, ... k, k represents the k-th monitoring point, and N represents the total number of sampling times; S220: using a particle expectation maximization algorithm, iterating an estimation process of a model parameter vector of the nonlinear random degradation model to obtain a maximum estimation result of the model parameter vector; S230: Calculate and obtain parameter estimation results using a nonlinear random degradation model parameter adaptive estimation algorithm based on particle filtering and the particle smoothing density; S240: Using the parameter estimation result, the maximum estimation result of the model parameter vector is updated, and the model parameter vector is obtained by a gradient descent search method.

5. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 4 is characterized in that: The expression of the maximum estimation result of the model parameter vector is: in, Indicates that based on the observed data Y 1:k The qth iteration result of represents the maximization parameter, It means to calculate about p(z k ,Y 1:k |Θ), p(z k ,Y 1:k |Θ) represents the joint likelihood function, z k represents the implicit state of the k-th monitoring point model, Y 1:k represents the actual observation data from the 1st point to the kth point, Θ represents the unknown parameter vector of the model, and q represents the number of iterations.

6. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 4 is characterized in that: The expression of the parameter estimation result is: in, represents the expectation of the joint likelihood function, Θ represents the unknown parameters of the model, Indicates that based on the observed data Y 1:k The qth iteration result of represents the conditional expectation of the joint likelihood function, p(z k ,Y 1:k |Θ) represents the joint likelihood function, z k represents the implicit state of the k-th monitoring point model, Y 1:k represents the actual observation data from the 1st point to the kth point, Θ represents the unknown parameters of the model, p(z1|z0,Θ) represents the prior distribution of the implicit state of the first monitoring point, z1 represents the implicit state of the first monitoring point, z0 represents the initial implicit state, p(z m+1 |z m ,Θ) represents the prior distribution of the implicit state of the m+1th monitoring point, z m+1 represents the implicit state of the mth monitoring point, z m represents the implicit state of the mth monitoring point, p(y m |z m ,Θ) represents the observation data y m The joint PDF of y m represents the observation data of the mth monitoring point, m represents the mth monitoring point, k represents the kth monitoring point, and q represents the number of iterations.

7. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 1, characterized in that: The gradient calculation expression of the model parameter vector is: in, represents the expectation of the joint likelihood function, Θ represents the unknown parameters of the model, Indicates that based on the observed data Y 1:k The qth iteration result of , q represents the number of iterations, and Represent the three parts of the joint log-likelihood function respectively.

8. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 1 is characterized in that: The S3 includes: According to the random degradation process, the remaining life function of the equipment is constructed; Based on the nonlinear random degradation model, the implicit state of the model is obtained by sampling the prior distribution, and the probability density function corresponding to the prior distribution function and the actual measurement data is obtained; Based on the prior distribution function and the probability density function corresponding to the actual measurement data, the posterior distribution function is approximated using standard importance weights; The model parameter vector, the equipment remaining life function and the posterior distribution function are used to adaptively predict the remaining life of the randomly degraded equipment by considering the influence of mixed measurement errors to obtain a remaining life prediction result.

9. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 1, characterized in that: The expression of the equipment remaining life function is: L k inf{l k :Y(l k +t k )≥w|Y(t k ) <w}; The expression of the probability density function corresponding to the actual measurement data is: The expression of the standard importance weight is: Among them, L k represents the remaining life of the kth monitoring point, inf represents the infimum, l k represents the remaining life of the kth monitoring point, Y(l k +t k ) indicates l k +t k The degenerate state corresponding to the moment, t k represents the duration corresponding to the kth monitoring point, w represents the failure threshold, Y(t k ) indicates t k The degenerate state corresponding to the moment, Represents the observed data y k The joint PDF of y k represents the observation data of the kth monitoring point, represents the implicit state, Θ represents the unknown parameter vector of the model, a represents the lower bound of the quantization error, b represents the upper bound of the quantization error, Indicates e k PDF, e k represents the quantization error, Represents ε k PDF, ε k represents the measurement error, σ ε represents the standard deviation of measurement error, exp represents the exponential form of a natural constant, represents the potential degradation state, q represents the quantization range, Φ represents the cumulative distribution function of the standard normal distribution, represents the k-th criterion importance weight, represents the k-1th standard importance weight, and Φ represents the cumulative distribution function of the standard normal distribution.

10. The method for predicting the remaining life of degraded equipment considering the influence of mixed measurement errors according to claim 1, characterized in that: The expression of the remaining life prediction result is: in, The PDF of the remaining life, L k Remaining life, l k represents the remaining life, Θ represents the unknown parameter vector of the model, Y 1:k represents the observation data of the 1st to kth monitoring points, represents the normalized weight, ω represents the failure threshold, represents the potential degradation state of the kth point, represents the k-th point drift coefficient, t k represents the kth point monitoring time, l k represents the remaining life, μ represents the nonlinear function form, τ represents time, θ represents the random parameter, exp represents the exponential function with e as the base, σ B represents the diffusion coefficient, i represents the i-th sampling, k represents the number of monitoring points, and N represents the number of sampling times.

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